A Novel Multi-Attribute Decision-Making Strategy for Industry 4.0 with Uncertainties using Rough Approximate Operators of Fermatean Fuzzy Hypersoft Sets

Managing uncertainties and computational complexities present significant challenges for decision-makers in blockchain technology, Industry 4.0, and the Circular Economy, all of which are essential for sustainable manufacturing. This research aims at developing an enhanced multi-attribute decision-making (MADM) method for supplier and process selection in smart factories to address uncertainties and promote sustainability objectives. Firstly, the approximate operators, i.e., upper and lower rough approximations, of Fermatean fuzzy hypersoft sets (FFHS), are developed and elaborated with understandable numerical examples. Some results of such operators are modified for aggregation operations. Additionally, for the sake of ranking, score function and ring sum operation in terms of such operators, are introduced. Secondly, an MADM system is established based on a robust algorithm which employs the proposed operators, score function and ring sum operation. To validate the algorithm, a hypothetical case study is presented for the evaluation of solution measures Integrating Industry 4.0, blockchain technology and the Circular Economy practices. The proposed framework efficiently detains various levels of uncertainty and ranks sustainable strategies within Industry 4.0. It utilizes fermatean hypersoft representation for significant uncertainty, encompassing membership and non-membership assessments with cube sum constraints. The method reinforces decision quality amidst imprecise data, aligning with green supplier selection literature. Designed for sustainability decision-making, it addresses gaps in managing ambiguous expert judgments and includes algorithmic procedures along with a detailed case study, providing a comprehensive decision support system for high-uncertainty manufacturing contexts.